Method, numerical control device and machine tool for machining a workpiece

ABSTRACT

Relative movement between a tool and a workpiece for machining the workpiece with a machine tool is controlled by defining a machine coordinate system (MKS) relative to a machine base of the machine tool and a rotation coordinate system (RKS) relative to the MKS by defining the origin of the RKS in the MKS, defining the orientation of a selected coordinate axis of the RKS in the MKS, defining an axis of rotation around which the RKS rotates in the MKS, defining an angular velocity with which the RKS rotates around the axis of rotation, defining a tool path in the RKS, and controlling the relative movement according to the defined tool path. With this procedure, complex movements of a machine tool, in particular in connection with so-called interpolation turning, can be described or programmed in a relatively simple manner.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the priority of European Patent Application,Serial No. EP 18177170.0, filed Jun. 12, 2018, pursuant to 35 U.S.C.119(a)-(d), the content of which is incorporated herein by reference inits entirety as if fully set forth herein.

BACKGROUND OF THE INVENTION

The present invention relates to a method and a numerical control devicefor controlling a relative movement between a tool and a workpiece formachining the workpiece using a machine tool. Furthermore, the inventionrelates to a machine tool for machining a workpiece using a tool, withat least three translational axes and at least one rotational axis, aswell as a tool spindle that can be rotated around a tool spindle axisfor the relative movement of a tool connected to the tool spindlerelative to a workpiece affixed to a workplace holder of the machinetool.

The following discussion of related art is provided to assist the readerin understanding the advantages of the invention, and is not to beconstrued as an admission that this related art is prior art to thisinvention.

In some machine tools known in the art, a tool spindle rotatessynchronously around a tool spindle axis and around an axis of rotationsuch that a tool cutting edge performs a turning process on a workpieceheld in a fixed position in the machine tool. Whereas in classicalturning, the contour of rotation is determined by the movement of thetool relative to the workpiece rotating around a workpiece axis, in thecase of interpolation turning known in the art, the tool moves with anoriented cutting edge around the axis of symmetry of the workpiece alongthe contour to be produced.

A disadvantage of the known method of interpolation turning is that, inorder to define the tool paths, special cycles must be used when cuttinga contour in a machining plane. Defining the tool paths is thereforecomplex and involves considerable effort.

It would therefore be desirable and advantageous to obviate prior artshortcomings and to provide an improved method for controlling a machinetool, a numerical control device, and a machine tool, which simplify thegeneration of tool paths for machining a workpiece.

SUMMARY OF THE INVENTION

According to one aspect of the present invention, a method forcontrolling a relative movement between a tool and a workpiece formachining the workpiece using a machine tool includes

-   -   defining a machine coordinate system (MKS) in relation to a        machine base of the machine tool,    -   defining a rotation coordinate system (RKS) in relation to the        machine coordinate system (MKS) by:        -   defining an origin of the rotation coordinate system (RKS)            in the machine coordinate system (MKS),        -   defining in the machine coordinate system (MKS) an            orientation of at least one selected coordinate axis of the            rotation coordinate system (RKS),        -   defining an axis of rotation about which the rotation            coordinate system (RKS) rotates in the machine coordinate            system (MKS),        -   defining an angular velocity with which the rotation            coordinate system (RKS) rotates about the axis of rotation,    -   defining at least one tool path in the rotation coordinate        system (RKS), and    -   controlling the relative movement according to the tool path        defined in the rotation coordinate system (RKS).

According to another aspect of the present invention, a numericalcontroller controlling relative movement between a tool and a workpiecefor machining the workpiece with a machine tool is configured to:

-   -   define a machine coordinate system (MKS) in relation to a        machine base of the machine tool,    -   define a rotation coordinate system (RKS) in relation to the        machine coordinate system (MKS) by:        -   define an origin of the rotation coordinate system (RKS) in            the machine coordinate system (MKS),        -   define in the machine coordinate system (MKS) an orientation            of at least one selected coordinate axis of the rotation            coordinate system (RKS),        -   define an axis of rotation about which the rotation            coordinate system (RKS) rotates in the machine coordinate            system (MKS),        -   define an angular velocity with which the rotation            coordinate system (RKS) rotates about the axis of rotation,    -   define at least one tool path in the rotation coordinate system        (RKS), and    -   control the relative movement according to the tool path defined        in the rotation coordinate system (RKS).

According to yet another aspect of the present invention, a machine toolfor machining a workpiece using a tool affixed to a workpiece holder ofthe machine tool includes:

-   -   a tool spindle rotatable about a tool spindle axis and holding a        tool constructed to machine the workpiece,    -   at least three translational axes and at least one rotational        axis, and    -   a numerical controller controlling a relative movement between        the tool and the workpiece,    -   wherein the numerical controller is configured to:        -   define a machine coordinate system (MKS) in relation to a            machine base of the machine tool,        -   define a rotation coordinate system (RKS) in relation to the            machine coordinate system (MKS) by:            -   define an origin of the rotation coordinate system (RKS)                in the machine coordinate system (MKS),            -   define in the machine coordinate system (MKS) an                orientation of at least one selected coordinate axis of                the rotation coordinate system (RKS),            -   define an axis of rotation about which the rotation                coordinate system (RKS) rotates in the machine                coordinate system (MKS),            -   define an angular velocity with which the rotation                coordinate system (RKS) rotates about the axis of                rotation,        -   define at least one tool path in the rotation coordinate            system (RKS), and        -   control the relative movement according to the tool path            defined in the rotation coordinate system (RKS).

The term “controlling” refers to its common use in control technology.However, the term also includes “regulating.”

As is common, a (fixed) machine coordinate system, hereinafter referredto as MKS, is defined in relation to a machine base of the machine tool.Advantageously a Cartesian coordinate system may be selected for thispurpose, which is aligned such that the coordinate axes are alignedparallel to three or the three translational axes (linear axes) of themachine tool. This reduces the computing effort to calculate theindividual axis movements to depart from a certain tool path. Inprinciple however it is possible to select any position of thecoordinate point of origin and orientations of the coordinate axes.

Furthermore, in the present invention, a rotation coordinate system,hereinafter referred to as RKS, is also defined in relation to themachine coordinate system. In principle, this can also be any coordinatesystem. Advantageously, however, a Cartesian coordinate system may beselected for this purpose. The coordinates of a point defined in the MKScan be specified in the RKS and vice versa through a correspondingcoordinate transformation. Points along the path, or tool paths, canaccordingly be transferred or translated from one coordinate system intoanother. The use of coordinate transformations hi machine tools isgenerally known and hence conventional.

In general, the present invention provides for the RKS to be defined inthe MKS by stipulating the coordinate point of origin with respect tothe MKS and by stipulating the orientation of at least one selectedcoordinate axis (for example the z′ axis) of the RKS. The orientationsof the two remaining coordinate axes can be defined in any way.Preferably three coordinate axes are defined in the RKS such that theyform a Cartesian coordinate system.

Furthermore, an axis of rotation around which the RKS rotates in theMKS, and an angular velocity with which the RKS rotates around the axisof rotation, are defined. Advantageously, an axis may be selected as theaxis of rotation that does not coincide with an axis of the MKS. Theangular velocity may also be defined so as to correlate with a spindlespeed of a tool spindle of the machine tool. In particular, the angularvelocity corresponds to the spindle speed.

With this procedure, workpiece contours or tool paths can be defined ordescribed makes for many uses of machine tool. In other words, therelative movements between the tool and the workpiece can be defined ordescribed in a relatively simple manner in the RKS, while producingrelatively complex movements of the machine axes or relatively complexmovements of the tool relative to the workpiece in the MKS.

Hereinafter, it will be assumed that both the MKS and the RKS areCartesian coordinate systems. However, the procedure demonstrated belowmay in principle be applied analogously to any coordinate systems. Theuse of Cartesian coordinate systems is common in connection with machinetools and facilitates the calculation of points on the path in differentcoordinate systems.

According to another advantageous feature of the present invention, atleast the position and orientation of the axis of rotation, but likewisealso the position and orientation of the RKS, may be aligned with aworkpiece machining axis. The workpiece machining axis is advantageouslyan axis of symmetry of a subsection of the workpiece (workpiece section)to be machined, which is at least substantially rotationallysymmetrical. This workpiece section is preferably to may be machined inaccordance with the invention by way of interpolation turning. Theworkpiece machining axis is determined from the geometric data of theworkpiece in conjunction with the clamping.

Advantageously, the axis of rotation may be aligned relative to theworkpiece such that the axis of rotation coincides with the workpiecemachining axis of the workpiece. The RKS then rotates around theworkpiece machining axis.

In a further simplification, the selected coordinate axis (z′) may beoriented parallel to the axis of rotation.

According to another advantageous feature of the present invention,especially when used with “Interpolation turning”, the coordinate pointof origin of the RKS may be defined in the MKS, for example byspecifying a displacement vector, such that the origin of the RKScoordinate system lies on the workpiece machining axis. In principle,any point on the workpiece machining axis can function as the origin ofthe RKS coordinate system.

Furthermore, the position and orientation of the selected coordinateaxis (z′ axis) may be selected so as to coincide with the workpiecemachining axis. As a result, turning cycles, which define for example acontour in the x-z plane and have already been created for conventionalturning tools, can be used for “interpolation turning” machining in theRKS.

Once a selected axis of the RKS (z′ axis) and the origin of the RKS havebeen defined, an orientation of a further axis (x axis) of the RKS canbe defined as a function of the type of rotation of the RKS (e.g. Euleror RPY) around the selected axis (z′ axis). Advantageously, the axes ofthe RKS are defined in relation to the position and orientation of thetool spindle axis in its starting position such that the tool spindleaxis lies in a plane spanned by the selected axis (z′) and the furtheraxis (x′). As is typical for turning, the tool is then moved in in thex′ direction at y=0.

Advantageously, the tool spindle axis may be aligned parallel to theselected axis (z′). This corresponds to the most common arrangement in aconventional turning tool.

With an active transformation and with the tool spindle switched on, thetool spindle advantageously rotates around the tool spindle axis andsynchronously the tool spindle axis rotates around the selected axis(z′) in relation to the MKS, so that as the tool spindle rotates aroundthe tool spindle axis, the tool spindle axis rotates around the selectedaxis (z′). As a result, during one rotation around the section of theworkpiece to be machined, the tool cutting edge is always aligned towardthe axis of symmetry of the section of the workpiece to be machined.However, in particular with a multi-edge tool, the rotational speeds mayalso differ from one another.

According to the present invention, rotationally symmetrical subsectionsof an intrinsically rotationally asymmetrical workpiece can be machinedrelatively easily using interpolation turning. In particular, a desiredcontour of the workpiece need no longer be divided in a multiplicity oftool paths through special cycles. Instead, simple turning cycles can beused for this purpose.

In many use cases, the machining axis of the workplace may be positionedin the x-y plane of the MKS by skillful clamping of the workpiece in themachine tool. The RKS then only has to be pivoted relative to the MKSaround one axis of the MKS so that the selected axis (z′) coincides withthe workpiece machining axis. By defining the orientation of theselected axis, the other two axes of the RKS are then also defined withrespect to the MKS. For this special case, it is therefore sufficient todefine the origin of the coordinate system and the orientation of theselected axis and to derive therefrom the position and orientation ofthe RKS in the MKS and consequently the coordinate transformation.

In order to reach a desired position and orientation of the selectedaxis (z′), However, it may also be necessary to rotate the RKS in spacerelative to the MKS around more than one axis. For example, the RKS canthen be derived from the MKS by specifying the displacement vector withrespect to the origin of the coordinate system and by specifying theso-called Euler angle. Coordinates of the RKS can then be converted intocoordinates of the MKS and vice versa.

The orientation of the selected axis (z′) is based on the workplacemachining axis. In principle, an infinite number of possibilities existfor orienting the two remaining axes—even when assuming a Cartesian RKS.In order to create a clear starting situation for machining theworkpiece, the orientation of a further axis of the RKS, for example thex′ axis, is therefore specified. The orientation of the remaining axis,in this example the y axis, is then also determined.

However, in the context of the invention, a static coordinatetransformation rather than a dynamic coordinate transformation isdetermined, because both an axis of rotation around which the RKSrotates in the MKS, preferably the z′ axis, and also an angular velocityfor the rotation are specified. This has the consequence that with anactive transformation, a fixed point in the RKS rotates around the axisof rotation from the perspective of the MKS with precisely this angularvelocity. The same is true for a position and orientation of a toolspindle or of a tool connected thereto which is fixed in space in theRKS. These also rotate with this angular velocity around the axis ofrotation when the transformation is activated.

Advantageously, before activating the coordinate transformation, i.e. inthe still static RKS, the spindle position and spindle orientation orthe tool position and the tool orientation, in other words the startingposition, are defined in the RKS. With an active transformation and witha synchronous rotation of the tool spindle in relation to the rotationof the RKS, the correct interpolation turning movement of the toolspindle is generated automatically.

According to another advantageous feature of the present invention, thetool spindle axis may be aligned parallel to the rotation axis of thecoordinate system.

According to another advantageous feature of the present invention, thetool, in particular a tool cutting edge, is oriented toward the axis ofrotation or in the opposite direction.

With the above assumptions, the tool movement in the RKS can bespecified in the same way as for a 2-axis turning tool having a simpleconstruction.

In the context of the invention, a—preferably rotationallysymmetrical—contour of a workpiece or workpiece section to be created isgenerally specified in the RKS. Next, tool paths for generating thespecified contour are calculated by using turning algorithms that areused for controlling or path generation in conventional turning tools.

In accordance with the invention, the tool paths are defined withrespect to the RKS and the relative movements between the tool andworkpiece are generated in accordance with the tool paths defined in theRKS. For this purpose, for the movement of the machine axes, each of thepoints on the path determined in the RKS are converted, using acorresponding coordinate transformation, into points on the path or axispositions of the MKS and moved to accordingly.

Advantageously, the introduction of an RKS according to the inventionenables specifying the position and/or orientation of the tool spindleaxis, the position and/or orientation of the tool, in particular a toolcutting edge, and the desired contour of the workpiece in the RKS. Thisis done analogously to the definition of the corresponding values for aconventional turning tool. Like with turning using a conventionalturning tool, defining the contour preferably takes place in the x′-z′plane of the RKS. Advantageously, the controller determines therefrom,initially also in the RKS, the tool paths required to produce thecontour.

The major difference compared to conventional interpolation turning isthat the coordinate transformation for defining the RKS in relation tothe MKS is not static but instead dynamic. Synchronously with therotation of the tool spindle, the RKS rotates in relation to the MKSaround the selected axis (z′ axis) of the RKS. From the perspective ofthe RKS, the corresponding coupling of the machine axes means that thetool spindle and in particular the tool are in a fixed position inrelation to the subsection of the workpiece to be machined, whereas thisworkpiece subsection rotates around its axis of symmetry, i.e. theworkpiece machining axis. From the perspective of the programmer, thestarting point is therefore the same as when turning with a conventionalturning tool. During the rotation of the tool spindle around the toolspindle axis and the rotation of the RKS in relation to the MKS, themachining paths of the tool (tool paths) defined in the RKS are nowtraversed in order to produce the desired workpiece contour.

A particular advantage of the inventive procedure for the user is thatexisting turning cycles programmed for turning with conventional turningtools can be used to determine tool paths. The creation of new,generally highly complex special cycles for interpolation turningconsequently becomes unnecessary for many applications. This is asignificant advantage in terms of cost and time.

As already described above, both the MKS and the RKS are preferablyCartesian coordinate systems. In principle, other coordinate systemscould be used in special cases for certain applications. Defining theorigin of the coordinate system and orienting the axes of the coordinatesystem in relation to the subsection of the workpiece to be machined areadvantageously done analogously to the corresponding selection whenturning with a conventional turning tool.

The mathematical background of the invention will be explained ingreater detail below. To this end, it is assumed that the kinematics ofthe machine can be described by a change of rotary axes, linear axes andconstant offsets.

In the context of the invention, it is necessary to move to a definedpoint on the workpiece with a defined spatial orientation. In general,in order to move to any point with any orientation, at least threedegrees of freedom of orientation and three degrees of freedom oftranslation are required.

Since orientations can only be changed by rotations, the kinematic chainmust contain at least three rotational axes in order to be able toassume any orientation in space.

In order for the problem to be uniquely solvable, the total number ofaxes must be at least six, at least three of which must be embodied asrotational axes (rotary axes), The remaining three axes may be (anycombination of) both rotary and also linear axes. There may be anynumber of constant offsets.

Note: the machine can also contain further (redundant) axes in thechain. Determining the axis positions is then no longer unambiguous, orfurther criteria must be used with these arrangements in order todetermine the position of these axes.

An example of a kinematic configuration with three linear axes and threerotary axes will be described below:

The parts at the beginning and end of the kinematic chain and betweenthe rotational axes are referred to as sections. In other words, thereare precisely four sections. Each of these sections can contain linearaxes (subject to the boundary condition that their total number isthree).

With the designations

{right arrow over (r_(n))} linear offsetA_(n) rotation (rotational machine axis){right arrow over (u)} tool vectorF rotation of the workpiece coordinate system vis-à-vis the MKS{right arrow over (f)} zero offset in the rotated workpiece coordinatesystemS rotation around the machining axis of the workpiece{right arrow over (p)} position of the machining point in workpiececoordinates the following applies:

{right arrow over (r ₁)}+ A ₁ *({right arrow over (r ₂)}+ A ₂ *({rightarrow over (r ₃)}+ A ₃ *({right arrow over (r ₄)}+{right arrow over(u)})))= F *({right arrow over (f)}+S (ωt)*{right arrow over (p)})  (1)

The linear offset {right arrow over (r_(n))} of the nth section isdefined as

{right arrow over (r _(n))}={right arrow over (c _(n))}+Σ_(i=1) ^(k)^(n) x _(n) _(i) *{right arrow over (e _(n) ₁ )}  (2)

where:{right arrow over (c_(n))} constant offsetk_(n) number of linear axes in the section n{right arrow over (e_(n) ₁ )}unit vector of the ith linear axes in thesection nx_(n) _(i) position of the ith linear axis in the section n.

For the determination of the angle of rotation of the rotations A_(n)(i.e. the orientation), in the above equation the displacements can bedisregarded provided that {right arrow over (u)} and {right arrow over(p)} are defined at the starting position hi the same coordinate systemas the position of the machining point. The (non-linear) matrix equation

A ₁ * A ₂ * A ₃ = F*S (ωt)  (3)

must then be solved. If the aforementioned condition is not met, afurther rotation is introduced in the above equation, which however onlycauses a modified constant rotation F and therefore does notsignificantly change the problem.

With known rotations, the positions of the three linear axes can then bedetermined as a solution to a (linear) system of equations.

When machining at the periphery of the part to be produced, the toolmust be guided with a constant orientation relative to the surface. Inthe case of a rotation at the periphery of the part, this means that thetool must also rotate around an axis that is parallel at all points intime to the machining axis of the workplace. Such a movement can becreated in accordance with (3) by controlling the rotations describedwith A₁ to A₃ as a function of time.

Of particular interest from a technical perspective, however, is thespecial case where the described rotation is performed in that only asingle rotary axis rotates, while the other two rotary axes do notchange their position during machining, i.e. they orient the third axissuch that it is parallel to the machining axis. This is typically thethird axis (A₃ ), which has to be implemented as a (position-controlled)spindle and which holds the tool.

It then follows from equation (3) for this special case that:

A ₁ * A ₂ = F =const. and A ₃ (ωt+φ ₀)= S (ωt)  (4)

This simplification is only possible if the tool can be correctlyoriented relative to the workpiece by a suitable selection of φ₀, i.e.when the machining axis and the axis of rotation are parallel.

BRIEF DESCRIPTION OF THE DRAWING

Other features and advantages of the present invention will be morereadily apparent upon reading the following description of currentlypreferred exemplified embodiments of the invention with reference to theaccompanying drawing, in which:

FIG. 1 shows a schematic diagram of a machine tool suitable forexecuting the present invention,

FIGS. 2 to 7 show measures for executing the method according to theinvention, and

FIG. 8 shows major method steps for executing the method according tothe present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Throughout all the figures, same or corresponding elements may generallybe indicated by same reference numerals. These depicted embodiments areto be understood as illustrative of the invention and not as limiting inany way. It should also be understood that the figures are notnecessarily to scale and that the embodiments are sometimes illustratedby graphic symbols, phantom lines, diagrammatic representations andfragmentary views. In certain instances, details which are not necessaryfor an understanding of the present invention or which render otherdetails difficult to perceive may have been omitted.

Turning now to the drawing, and hi particular to FIG. 1, there is showna schematic, highly simplified diagram of an embodiment of the inventionwith a machine tool 1 having three translational axes L1, L2 and L3(linear axes) configured to move a tool 2 relative to a workpiece 3 inthree linear spatial axes. The machine tool 1 includes a (fixed) machinebase 4 to which a workpiece holder 5 is affixed. One point on the fixedmachine base 4 is selected as a reference point (origin) for an MKS(also fixed) with the coordinate axes x, y and z. The coordinate axes x,y and z of the MKS are advantageously selected such that the x axis isaligned parallel to L1, the y axis is aligned parallel to L2 and the zaxis is aligned parallel to L3, Furthermore, a tool head that can bepivoted around a rotational axis B (rotary axis), with which the tool 2can be pivoted around a B axis that is parallel to the y axis, isprovided on the machine tool 1. The tool 2 is affixed to a tool spindle6 enclosed within the tool head 10 and can be rotated around a toolspindle axis SA. Like the other axes, the tool spindle 6 is providedwith a position-controlled drive such that any angle can be set for thetool spindle 6 and as a result a cutting edge 7 of the workpiece 2 canbe oriented with respect to the tool spindle axis SA. A numericalcontroller 8 is provided for the coordinated position control of theindividual axes of the machine tool 1.

FIGS. 2 to 7 show in more detail a process according to the presentinvention for turning the workpiece 3 shown in the exemplary embodimentof FIG. 1 when clamped, To this end, FIG. 2 once more shows the MKS withthe coordinate axes x, y and z and the rotationally asymmetricalworkpiece 3 clamped in a fixed position in the machine tool with aworkpiece section 9 to be machined, which is rotationally symmetricalwith respect to a workpiece machining axis WA.

In accordance with the invention, a Cartesian RKS with the coordinateaxes x′, y′ and z′ is first defined for the machining of the workpiece 3to be performed. As can be seen in FIG. 3, for this purpose adisplacement vector {right arrow over (v)} for the coordinate point oforigin is first determined such that the origin 0′ of the RKS coordinatesystem lies on the workpiece machining axis WA of the workpiece 3. Inthe exemplary embodiment, the workpiece machining axis WA is an axis ofsymmetry of a workpiece section 9 which is to be machined in accordancewith the invention.

Furthermore—as can be seen in FIG. 4—the z′ axis is oriented such thatlies on the workpiece machining axis WA of the workpiece 3. In thisexemplary embodiment, the workpiece machining axis WA lies in the x-zplane of the MKS after corresponding positioning and orientation of theworkpiece 3. The orientation of the z′ axis is then produced from theMKS by means of a single pivoting movement of the z axis around the yaxis. It is therefore sufficient to specify a single angle φ throughwhich the x′ axis and the z′ axis must be pivoted around the y′ axis inorder to define the orientation of the RKS in the MKS. If the workpiecemachining axis WA did not lie in the x-z plane of the MKS, at least onefurther pivoting movement would be necessary in order to cause the z′axis to He on the workpiece machining axis WA.

Assuming that the x′ axis should also lie in the x-z plane, theorientations of the x′ axis and y′ axis and therefore the whole RKS arethen also determined unambiguously in relation to the MKS.

In the inventive procedure, the tool paths for machining the workpiece 3are specified not in the MKS, but rather in the RKS. FIG. 5 illustratesthe starting situation for this purpose, in which the position andorientation of the tool head 10 and in particular of the tool cuttingedge 7 are specified in the RKS. In the advantageous starting positionin accordance with FIG. 5, the spindle axis SA lies in the x′-z′ planeand is oriented parallel to the z axis. The tool 2 is oriented oppositeto the x′ direction.

According to a particular feature of the coordinate transformation inaccordance with the invention, the RKS defined as described above nowrotates continuously with a constant angular velocity ω around the z′axis. This causes a constant position and orientation of the tool 2specified in the RKS to perform, from the perspective of the MKS, acircular movement of the tool 2 with the angular velocity ω around thez′ axis, with the orientation of the cutting edge 7 thus also changingwith the angular velocity ω. The angular velocity ω′, with which thetool spindle rotates 6 around the tool spindle axis SA, is henceidentical to the angular velocity ω with which the RKS rotates aroundthe z′ axis. The rotation of the tool spindle 6 is therefore synchronouswith the rotation of the RKS. In the exemplary embodiment, the cuttingedge 7 therefore remains oriented parallel to the x′ axis at all times,such that the cutting edge 7 points at all times toward the z axis asthe tool 2 rotates. This is illustrated in FIGS. 6 and 7, which show theworkpiece machining at two different points in time. An observer movingin conjunction with the RKS therefore sees a fixed tool with a constantorientation and a workpiece section 9 rotating around the z′ axis.However this represents the typical starting situation for the machiningmode “turning” when using a conventional turning tool.

Starting from this starting situation, the (rotationally symmetrical)contour of the workpiece section 9 to be machined is specified in thex′-z′ plane. The tool paths are then calculated in the controller 8 fromthe specified contour as with a conventional turning tool, Taking intoconsideration the coordinate transformation described above, thecontroller 8 then converts the tool paths calculated for the RKS intotool paths with respect to the MKS and the corresponding coordinatedmovements of the relevant machine tool axes L1 to L3 and B of themachine tool 1.

FIG. 8 illustrates major method steps in the execution of a methodaccording to the invention. In a first method step S1, an MKS that isfixed with respect to the employed machine tool is defined. In a methodstep S2, a workpiece machining axis is defined for a workpiece sectionof the workpiece to be machined, with the workpiece to be machined beingclamped in the machine tool. The workpiece machining axis is an axis ofsymmetry of the workpiece section of the workpiece to be machined. In amethod step S3, the origin of an RKS is defined on the workpiecemachining axis in the MKS, for example by defining a displacementvector. In a method step S4, the orientation of the RKS in relation tothe MKS is defined, for which typically three pivoting movements arerequired. For the special case in which the workpiece machining axislies in the x-z plane of the MKS, a rotation around the y axis issufficient so that the z′ axis of the RKS coincides with the workpiecemachining axis. In a method step S5, the tool path is defined in theRKS, preferably with respect to the axes x′ and z′ where y=0. Thedefinition of the tool path then largely corresponds to that used in thecase of “normal” turning. In a method step S6, the rotation of the toolspindle is started with the angular velocity ω, In a method step S7, therotation of the RKS about the z′ axis with the angular velocity ω′ isstarted simultaneously. Preferably ω′=ω. These rotations cause the toolwith the oriented cutting edge to rotate around the workpiece section tobe machined. Finally, in a method step S8, the tool path specified instep 5 is traversed.

A significant advantage achieved by the invention compared toconventional “interpolation turning” is that existing turning cycles orexisting tool paths for turning can be used, and these need only bespecified in the RKS. The transformation then allows the machine toexecute intrinsically complex axis movements that result in the desiredmachining, but specifying these axis movements in the RKS is relativelysimple and largely corresponds to the guidelines used with conventional“turning”.

The basic principle illustrated by the exemplary embodiment can also beapplied analogously to more complex machining processes. In particular,it is not essential for the workpiece machining axis to lie in the x-zplane of the MKS. In principle, the workpiece machining axis can lieanywhere in the machine tool working area. However, at least oneadditional rotary axis of the machine tool may then be required, forexample an A axis for executing a pivoting movement of the tool aboutthe x axis or an axis parallel to the x axis.

With respect to the coordinate transformation, a displacement andorientation of the RKS with respect to the MKS in three-dimensionalspace would generally be required, which causes greater computingcomplexity in the controller and more complex machine movements comparedwith the exemplary embodiment. However this in no way affects theadvantages for the user of a machine tool configured in this way.

While the invention has been illustrated and described in connectionwith currently preferred embodiments shown and described in detail, itis not intended to be limited to the details shown since variousmodifications and structural changes may be made without departing inany way from the spirit and scope of the present invention. Theembodiments were chosen and described in order to explain the principlesof the invention and practical application to thereby enable a personskilled in the art to best utilize the invention and various embodimentswith various modifications as are suited to the particular usecontemplated.

What is claimed as new and desired to be protected by Letters Patent isset forth in the appended claims and includes equivalents of theelements recited therein:

What is claimed is:
 1. A method for controlling a relative movementbetween a tool and a workpiece to be machined with a machine tool, themethod comprising: defining a machine coordinate system (MKS) inrelation to a machine base of the machine tool, defining a rotationcoordinate system (RKS) in relation to the machine coordinate system(MKS) by: defining an origin of the rotation coordinate system (RKS) inthe machine coordinate system (MKS), defining in the machine coordinatesystem (MKS) an orientation of at least one selected coordinate axis ofthe rotation coordinate system (RKS), defining an axis of rotation aboutwhich the rotation coordinate system (RKS) rotates in the machinecoordinate system (MKS), defining an angular velocity with which therotation coordinate system (RKS) rotates about the axis of rotation,defining at least one tool path in the rotation coordinate system (RKS),and controlling the relative movement according to the tool path definedin the rotation coordinate system (RKS).
 2. The method of claim 1,further comprising: defining a workpiece machining axis of a workpiecesection of the workpiece to be machined with the tool, and aligning theaxis of rotation relative to the workpiece such that the axis ofrotation lies on the workpiece machining axis.
 3. The method of claim 2,wherein the workpiece machining axis is an axis of symmetry of theworkpiece section.
 4. The method of claim 1, wherein the selectedcoordinate axis is oriented parallel to the axis of rotation.
 5. Themethod of claim 1, wherein the position and orientation of the rotationcoordinate system (RKS) is specified in the machine coordinate system(MKS) such that the selected coordinate axis lies on the axis ofrotation.
 6. The method of claim 1, wherein the machine coordinatesystem (MKS) and/or the rotation coordinate system (RKS) are realized asCartesian coordinate systems.
 7. The method of claim 1, wherein the toolis moved relative to the workpiece by way of at least threetranslational axes and at least one rotational axis.
 8. The method ofclaim 1, further comprising affixing the tool in a tool spindle forrotation about a tool spindle axis.
 9. The method of claim 8, wherein aposition and an orientation of the tool spindle axis is defined in therotation coordinate system (RKS).
 10. The method of claim 9, wherein thetool spindle is aligned relative to the rotation coordinate system (RKS)such that the tool spindle axis lies in a plane defined by twocoordinate axes of the rotation coordinate system (RKS).
 11. The methodof claim 10, wherein the tool spindle is aligned parallel to theselected coordinate axis of the rotation coordinate system (RKS). 12.The method of claim 1, further comprising specifying an orientation of acutting edge of the tool in the rotation coordinate system (RKS),wherein the tool path includes the orientation of the cutting edge. 13.The method of claim 12, wherein the orientation of the cutting edge inthe rotation coordinate system (RKS) is retained during machining of theworkpiece.
 14. The method of claim 2, wherein the tool path isdetermined based on a specified contour of the workpiece section
 15. Themethod of claim 1, wherein the tool path is defined by a turning cycleprogrammed for a conventional turning tool operation.
 16. A numericalcontroller controlling a relative movement between a tool and aworkpiece to be machined with a machine tool, the numerical controllerconfigured to: define a machine coordinate system (MKS) in relation to amachine base of the machine tool, define a rotation coordinate system(RKS) in relation to the machine coordinate system (MKS) by: define anorigin of the rotation coordinate system (RKS) in the machine coordinatesystem (MKS), define in the machine coordinate system (MKS) anorientation of at least one selected coordinate axis of the rotationcoordinate system (RKS), define an axis of rotation about which therotation coordinate system (RKS) rotates in the machine coordinatesystem (MKS), define an angular velocity with which the rotationcoordinate system (RKS) rotates about the axis of rotation, define atleast one tool path in the rotation coordinate system (RKS), and controlthe relative movement according to the tool path defined in the rotationcoordinate system (RKS).
 17. The numerical controller of claim 16,wherein a selected coordinate axis of the rotation coordinate system(RKS) is defined as the axis of rotation.
 18. The numerical controllerof claim 16, wherein the machine coordinate system (MKS) and/or therotation coordinate system (RKS) are Cartesian coordinate systems. 19.The numerical controller of claim 16, wherein an orientation of at leastone cutting edge of the tool is defined in the rotation coordinatesystem (RKS), and wherein the tool path includes the orientation of theat least one cutting edge.
 20. The numerical controller of claim 19,wherein the orientation of the at least one cutting edge in the rotationcoordinate system (RKS) is constant during machining of the workpiece.21. The numerical controller of claim 16, wherein the axis of rotationis aligned relative to the workpiece such that the axis of rotation lieson a workpiece machining axis of a workpiece section of the workpiece tobe machined by the tool.
 22. The numerical controller of claim 21,wherein the workpiece machining axis is defined as an axis of symmetryof the workpiece section of the workpiece to be machined by the tool.23. The numerical controller of claim 16, wherein the tool is affixed ina tool spindle for rotation about a tool spindle axis, and wherein thetool spindle is aligned relative to the rotation coordinate system (RKS)such that the tool spindle axis lies in a plane defined by twocoordinate axes of the rotation coordinate system (RKS).
 24. A machinetool for machining a workpiece affixed to a workpiece holder of themachine tool, comprising: a tool spindle rotatable about a tool spindleaxis and holding a tool constructed to machine the workpiece, at leastthree translational axes and at least one rotational axis, and anumerical controller controlling a relative movement between the tooland the workpiece, wherein the numerical controller is configured to:define a machine coordinate system (MKS) in relation to a machine baseof the machine tool, define a rotation coordinate system (RKS) inrelation to the machine coordinate system (MKS) by: define an origin ofthe rotation coordinate system (RKS) in the machine coordinate system(MKS), define in the machine coordinate system (MKS) an orientation ofat least one selected coordinate axis of the rotation coordinate system(RKS), define an axis of rotation about which the rotation coordinatesystem (RKS) rotates in the machine coordinate system (MKS), define anangular velocity with which the rotation coordinate system (RKS) rotatesabout the axis of rotation, define at least one tool path in therotation coordinate system (RKS), and control the relative movementaccording to the tool path defined in the rotation coordinate system(RKS).